Viewed as a quantum mechanical process, a photon travelling through the medium may either produce a phonon by exciting the lattice (known as the Stokes process), and thus lose energy, or absorb a phonon from the lattice (known as the Anti-Stokes process) and gain energy.

We require that momentum be conserved in the plane of the surface, so that:

pisinθ ± ps = - pssinθ.

kisinθ ± Q = - kssinθ.

We also require that energy be conserved, so that:

ωi ± Ω = &omegas.

In each case + Q or + Ω corresponds to absorbing a phonon while - Q or - Ω corresponds to creating one. Now, ± Ω = ωs - ωi = Δω. Furthermore, since the wavelength of light is much shorter than that of the phonon, we can make the approximation that kf ≅ - ki. So:

± Ω = Δω

Q = 2 kisinθ

Now the phonon travels at speed v, and Ω = v Q, so Q = Ω / v, and we get that

Δω = ± 2 v kisinθ

Thus if we measure the frequency shift Δω at various angles θ, we can plot Δω against sinθ to obtain a slope of 2 ki v. Knowing ki we can then determine v, the velocity of sound in the medium.

Once v is determined, and if the density of the material is known, the material's Young's modulus can be determined. Also, the frequency shift is dependent on the orientation of the crystal plane with respect to the incident light. By performing the experiment at various azimuthal angles as well as incident angles, other elastic constants such as C11, C12 and C44 can be determined.